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Figure 1: Space debris orbiting Earth.
Image from MIT news website depicting space debris orbiting the Earth at ~17,500 mph.



Executive Summary

  • Charged with informing the process to develop a debris on debris collision warning threshold to mitigate future collision risk and limit false alarms.

  • The study has focused on the following parameters:
    • Debris collision results in at least 1, 10, and 100 fragments at least five centimeters in diameter.
    • 5, 4, and 3 days to time of closest approach (TCA).
    • Concern Events terminology defined as Collision Probability \(\bf{\ge\text{1e-5}}\) within a day to TCA.

  • Final study implementations:
    • Removed all observations with \(\bf{\le 1\text{e-}10}\) Collision Probability.
    • Tested Warning Thresholds between \(\bf{1\text{e-8}\text{ and }1\text{e-5}}\).
    • Evaluated Missed Alert verse False Alarm risk at 5, 4 and 5, and 3,4 and 5 days to TCA.
    • Evaluated Short Notice Missed Alert verse False Alarm risk at 4, 3, and 2 days to TCA.

  • Conclusions
    • Performance increases as days to TCA decreases.
    • Optimal Warning Thresholds depend on days to TCA.
    • Variability in Collision Probability decreases as days to TCA decreases.

Problem Formulation

  • Problem Statement: Under what circumstances should debris-on-debris collision warnings be used?
    • What probability of collision should be used as a surrogate for an actual event of concern?
    • What probability of collision should trigger a warning at five, four and three days to TCA?
    • How well can we do in warning for events occurring in the future?

  • Mission Statement: Recommend debris collision notification thresholds and develop a mechanism to explore the notification decision space to assess risk of debris-on-debris collisions in space.

Exploratory Data Analysis

  • Questions:
    • How is the Collision Probability distributed?
    • How does the Collision Probability change over time?

  • Data Preparation:
    • Summarize by each event to show the Collision Probability for each fragment size at the last recorded time, if that time is within a day of TCA.
    • Summarize by each event to show the Collision Probability for each fragment size at the last recorded time, for each binned days to TCA.

Collision Probability Density

We need to find a range of values to appropriately label events of concern.


Figure 2: Collision Probability within One Day of TCA



We use,

\(\bf{\text{Collision Probabilty} \ge 1\text{e-7} \text{ and days to TCA} < 1 \text{ day,}}\)


as a surrogate to label a concern event.


Collision Probability Variability

  • Does the Collision Probability increase as we approach TCA?
  • Should we expect to have a lower warning threshold at five days to TCA?


Figure 3: Collision Probability as TCA Varies



Conclusions:

  • The variability tightens slightly around 0 as TCA approaches.
  • Some evidence of a slight decrease in Collision Probability as TCA approaches.
  • No compelling evidence of an advantage in significantly varying Warning Threshold.
  • We use:


\(\bf{1\text{e-8} \le Pc\_warn \le 1\text{e-5}}\),


where \(\bf{Pc\_warn}\) is the Collision Probability that triggers a warning.


Risk Tradespace

We need to evaluate warning thresholds by examining the trade space between risk aversion and tolerance.

We have the following working definitions:

\(\hspace{2.5cm}\bf{\text{Concern Event} := \text{Collision Probability} \ge 1\text{e-}5 \text{ and days to TCA < 1 day}}\)
\(\hspace{2.5cm}\bf{\text{False Negative (FN)} := \text{# of Concern Events in a year that did not trigger a warning}}\)
\(\hspace{2.5cm}\bf{\text{False Positive (FP)} := \text{# of False Alarms in a year}}\).

We can now explore how the warning threshold affects the \(\text{FP}\) and \(\text{FN}\).


Five days to TCA

Figure 4: Warning Performance at Five Days to TCA

Four days to TCA

Figure 5: Warning Performance at Four Days to TCA

Three days to TCA

Figure 6: Warning Performance at Three Days to TCA

Risk Tradespace with Uncertainty

Taking the optimal warning thresholds for each fragment size and days to TCA, we evaluate the performance on random data samples, and computing the 95% Confidence Interval for FN and FP counts. The boxes indicate the 95% bounds and the dot is the observed performance.

Figure 7: Warning Performance at Three, Four and Five Days to TCA

Way Forward

  • Stuff and things

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